Hypergraph Neural Networks

Sensor networks increasingly govern modern infrastructure, yet the data they lose are rarely missing in the uniform-random patterns assumed by standard imputation benchmarks. Loop detectors go offline during calibration, roadside cabinets silence clusters of nearby sensors, and newly installed instruments provide no history. Such failures create structured absences whose values are constrained by higher-order relations among groups of sensors, not merely by pairwise proximity. Existing low-rank and graph-based methods often miss this collective structure and can fail when missingness becomes coherent. We introduce Multi-Scale Hypergraph Laplacians (MSHL), a two-stage framework for learning higher-order structure from incomplete spatiotemporal observations. The Discovery stage builds a multi-scale hypergraph from complementary topology and residual-correlation evidence, with an observation-only selector that adapts to the supported interaction scale. The Refinement stage adds a small hypergraph-conditioned residual network that is safe by construction: it learns nonlinear corrections where informative residual features exist and defers to the linear estimate where they do not. We prove that MSHL represents group-conservation patterns inaccessible to pairwise graph priors, adapts to the best fixed scale up to a logarithmic factor, transfers this advantage to held-out imputation error, and admits a one-sided refinement guarantee. On two real traffic networks evaluated across scattered cell missingness, contiguous block outages, and whole-sensor blackouts at five rates, MSHL improves over a pairwise-graph baseline whenever higher-order structure is identifiable and otherwise matches it within sampling noise. The results point to a broader principle for reliable infrastructure learning: missing data should be treated not as isolated entries to fill, but as evidence of structure to discover.

Hypergraphs model higher-order relations that drive real-world decisions, from drug prescriptions to recommendations. A central structural signal in such data, beyond what pairwise relations can express, is interaction compositionality: whether a higher-order relation is compositional, emergent, or inhibitory with respect to its observed or unobserved sets. In polypharmacy, the regime decides whether a drug should be dropped, kept, or excluded: a compositional drug triple can be safely simplified, an emergent triple requires all drugs jointly, and an inhibitory triple flags a drug that disrupts an existing interaction. However, existing hypergraph learning methods, which merely propagate messages over observed hyperedges, leave this compositional signal unmodeled, allowing dangerous drug combinations to slip through and be misclassified. To this end, we propose the Hypergraph Pattern Machine (HGPM), shifting the paradigm from message passing to learning the compositional pattern of subsets. It tokenizes compositional subsets, organizes them in an inclusion DAG, and trains an inclusion-aware Transformer under masked reconstruction. On ten hypergraph benchmarks, HGPM matches or exceeds state-of-the-art methods. Notably, in a real adverse-event prediction case, HGPM correctly identifies the drug addition that inhibits the side effect among feature-identical candidates, a discrimination existing methods cannot make. The code and data are in https://github.com/KryieZhao/HGPM.git.

Hypergraphs provide a natural framework to model higher-order interactions in scientific, social, and biological systems. Hypergraph neural networks (HGNNs) aim to learn from such data, yet it remains unclear which higher-order structures these models can represent. We show that hypergraph expressivity is governed by which small patterns an architecture can detect and count. We formalize this via homomorphism densities, which measure how often a structural motif appears in a hypergraph. Combining classical homomorphism-count completeness with invariant approximation, we show that homomorphism densities generate all continuous hypergraph invariants and organize them into a strict hierarchy indexed by hypertree width. This yields a Width Wall: a fundamental architectural limit beyond which no hidden dimension, training procedure or fixed-depth HGNN can represent invariants requiring wider patterns. Our framework provides a unified characterization of 15 HGNN architectures, precisely identifies information lost by clique expansion, and motivates density-aware models that extend expressivity beyond bounded-width message passing. We experimentally validate this finding on an APPLICATION NODE CLASSIFICATION SUITE of real-world hypergraphs, where the Width Wall predicts when graph-reduction baselines fail and when density features help.

The increasing prevalence of large-scale hypergraphs poses significant computational challenges for hypergraph neural network (HNN) training. To address this, hypergraph condensation (HGC) distills large real hypergraphs into compact yet informative synthetic ones, beyond graph condensation (GC) methods limited to pairwise relations. However, existing HGC methods rely on decoupled training architectures, where structure generators are pre-trained on the original hypergraph but not jointly optimized with condensed features during refinement, resulting in misaligned structures that degrade downstream utility. Moreover, trajectory-based optimization incurs substantial computational overhead in refinement, limiting condensation efficiency. To tackle these issues, we propose \textbf{A}nchor-guided \textbf{H}yper\textbf{G}raph \textbf{C}ondensation with \textbf{D}ual-level \textbf{D}iscrimination (\textbf{AHGCDD}), which consists of three key components: (1) a node initialization module based on Heat Kernel PageRank (HKPR) to encode structural knowledge into feature semantics; (2) an anchor-guided hyperedge synthesis strategy for joint optimization of condensed features and structure; (3) a theoretically grounded dual-level discrimination objective for utility-preserving condensation without redundant HNN training. Extensive experiments demonstrate the superior effectiveness and efficiency of AHGCDD.

Graph neural networks have been widely used in Boolean satisfiability (SAT) tasks to learn structural information from SAT formulas. The goal of these studies is to solve SAT instances or to enhance SAT solvers, including tasks such as unsat-core prediction. However, most existing approaches model a SAT formula as a bipartite graph or a directed acyclic graph, which are less direct in capturing clause-level and higher-order interactions among literals and clauses. Moreover, these approaches are limited in modeling intrinsic polarity-related properties of SAT, such as the complementary relationship between the positive and negative literals of a variable. To address these limitations, we propose a polarity-aware representation learning framework over clause-literal hypergraphs. We model SAT formulas as clause-literal hypergraphs augmented with a clause incidence graph to capture higher-order structural interactions. We then introduce a polarity-aware decomposition mechanism that separates variable representations into polarity invariant and equivariant components, explicitly modeling the relationship between positive and negative literals, with the resulting literal representations propagated along the hypergraph structure. We further incorporate a polarity-inversion consistency regularization to reinforce polarity-consistent representations during training. Experimental results on multiple SAT datasets demonstrate the effectiveness of the proposed approach.

Accurate lesion segmentation is crucial for clinical diagnosis and treatment planning. However, lesions often resemble surrounding tissues and exhibit ill-defined boundaries, leading to unstable predictions in boundary/transition regions. Moreover, small-lesion cues can be diluted by multi-scale feature extraction, causing under- or over-segmentation. To address these challenges, we propose an Uncertainty-Aware Hypergraph Refinement Network (UHR-Net). First, we introduce an Uncertainty-Oriented Instance Contrastive (UO-IC) pretraining strategy that couples geometry-aware copy-paste augmentation with hard-negative mining of lesion-like background regions to improve instance-level discrimination for small and visually ambiguous lesions. Second, we design an Uncertainty-Guided Hypergraph Refinement (UGHR) block, which derives an entropy-based uncertainty map from a coarse probability map to guide hypergraph refinement. By splitting hyperedge prototypes into foreground and background groups, UGHR decouples higher-order interactions and improves refinement in ambiguous regions. Experiments on five public benchmarks demonstrate consistent gains over strong baselines. Code is available at: https://github.com/CUGfreshman/UHR-Net.

It remains challenging to assess driver fatigue from untrimmed videos under constrained computational budgets, due to the difficulty of modeling long-range temporal dependencies in subtle facial expressions. Some existing approaches rely on computationally heavy architectures, whereas others employ traditional lightweight pairwise graph networks, despite their limited capacity to model high-order synergies and global temporal context. Therefore, we propose HST-HGN, a novel Heterogeneous Spatial-Temporal Hypergraph Network driven by Bidirectional State Space Models. Spatially, we introduce a hierarchical hypergraph network to fuse pose-disentangled geometric topologies with multi-modal texture patches dynamically. This formulation encapsulates high-order synergistic facial deformations, effectively overcoming the limitations of conventional methods. In temporal terms, a Bi-Mamba module with linear complexity is applied to perform bidirectional sequence modeling. This explicit temporal-evolution filtering enables the network to distinguish highly ambiguous transient actions, such as yawning versus speaking, while encompassing their complete physiological lifecycles. Extensive evaluations across diverse fatigue benchmarks demonstrate that HST-HGN achieves state-of-the-art performance. In particular, our method strikes a balance between discriminative power and computational efficiency, making it well-suited for real-time in-cabin edge deployment.

Longitudinal neuroimaging is essential for modeling disease progression in Alzheimer's disease (AD), yet irregular sampling and missing visits pose substantial challenges for learning reliable temporal representations. To address this challenge, we propose SDE-HGNN, a stochastic differential equation (SDE)-driven spatio-temporal hypergraph neural network for irregular longitudinal fMRI connectome modeling. The framework first employs an SDE-based reconstruction module to recover continuous latent trajectories from irregular observations. Based on these reconstructed representations, dynamic hypergraphs are constructed to capture higher-order interactions among brain regions over time. To further model temporal evolution, hypergraph convolution parameters evolve through SDE-controlled recurrent dynamics conditioned on inter-visit intervals, enabling disease-stage-adaptive connectivity modeling. We also incorporate a sparsity-based importance learning mechanism to identify salient brain regions and discriminative connectivity patterns. Extensive experiments on the OASIS-3 and ADNI cohorts demonstrate consistent improvements over state-of-the-art graph and hypergraph baselines in AD progression prediction. The source code is available at https://anonymous.4open.science/r/SDE-HGNN-017F.

Recent advances in multi-modal detection have significantly improved detection accuracy in challenging environments (e.g., low light, overexposure). By integrating RGB with modalities such as thermal and depth, multi-modal fusion increases data redundancy and system robustness. However, significant challenges remain in effectively extracting task-relevant information both within and across modalities, as well as in achieving precise cross-modal alignment. While CNNs excel at feature extraction, they are limited by constrained receptive fields, strong inductive biases, and difficulty in capturing long-range dependencies. Transformer-based models offer global context but suffer from quadratic computational complexity and are confined to pairwise correlation modeling. Mamba and other State Space Models (SSMs), on the other hand, are hindered by their sequential scanning mechanism, which flattens 2D spatial structures into 1D sequences, disrupting topological relationships and limiting the modeling of complex higher-order dependencies. To address these issues, we propose a multi-modal perception network based on hypergraph theory called M2I2HA. Our architecture includes an Intra-Hypergraph Enhancement module to capture global many-to-many high-order relationships within each modality, and an Inter-Hypergraph Fusion module to align, enhance, and fuse cross-modal features by bridging configuration and spatial gaps between data sources. We further introduce a M2-FullPAD module to enable adaptive multi-level fusion of multi-modal enhanced features within the network, meanwhile enhancing data distribution and flow across the architecture. Extensive object detection experiments on multiple public datasets against baselines demonstrate that M2I2HA achieves state-of-the-art performance in multi-modal object detection tasks.

Online financial services constitute an essential component of contemporary web ecosystems, yet their openness introduces substantial exposure to fraud that harms vulnerable users and weakens trust in digital finance. Such threats have become a significant web harm that erodes societal fairness and affects the well-being of online communities. However, existing detection methods based on graph neural networks (GNNs) struggle with two persistent challenges: (1) long-tailed data distributions, which obscure rare but critical fraudulent cases, and (2) fraud camouflage, where malicious transactions mimic benign behaviors to evade detection. To fill these gaps, we propose HIMVH, a Hippocampus-Inspired Multi-View Hypergraph learning model for web finance fraud detection. Specifically, drawing inspiration from the scene conflict monitoring role of the hippocampus, we design a cross-view inconsistency perception module that captures subtle discrepancies and behavioral heterogeneity across multiple transaction views. This module enables the model to identify subtle cross-view conflicts for detecting online camouflaged fraudulent behaviors. Furthermore, inspired by the match-mismatch novelty detection mechanism of the CA1 region, we introduce a novelty-aware hypergraph learning module that measures feature deviations from neighborhood expectations and adaptively reweights messages, thereby enhancing sensitivity to online rare fraud patterns in the long-tailed settings. Extensive experiments on six web-based financial fraud datasets demonstrate that HIMVH achieves 6.42% improvement in AUC, 9.74% in F1 and 39.14% in AP on average over 15 SOTA models.

The application of learning based methods to vehicle routing problems has emerged as a pivotal area of research in combinatorial optimization. These problems are characterized by vast solution spaces and intricate constraints, making traditional approaches such as exact mathematical models or heuristic methods prone to high computational overhead or reliant on the design of complex heuristic operators to achieve optimal or near optimal solutions. Meanwhile, although some recent learning-based methods can produce good performance for VRP with straightforward constraint scenarios, they often fail to effectively handle hard constraints that are common in practice. This study introduces a novel end-to-end framework that combines constraint-oriented hypergraphs with reinforcement learning to address vehicle routing problems. A central innovation of this work is the development of a constraint-oriented dynamic hyperedge reconstruction strategy within an encoder, which significantly enhances hypergraph representation learning. Additionally, the decoder leverages a double-pointer attention mechanism to iteratively generate solutions. The proposed model is trained by incorporating asynchronous parameter updates informed by hypergraph constraints and optimizing a dual loss function comprising constraint loss and policy gradient loss. The experiment results on benchmark datasets demonstrate that the proposed approach not only eliminates the need for sophisticated heuristic operators but also achieves substantial improvements in solution quality.

Bundle recommendation ranks sets of related items rather than isolated items. Its central challenge is to connect user preferences, item interactions, and bundle composition without losing the signals needed to rank bundles. We propose Hypergraph-Enhanced Dual Convolutional Neural Network (HED), which constructs a complete hypergraph containing user--bundle, user--item, and bundle--item interactions together with intra-user and intra-bundle relations. HED couples complete-hypergraph propagation with a user--bundle branch, allowing item-aware higher-order context to inform ranking while preserving recommendation-specific signals. On NetEase, HED-128 improves over the strongest baseline by 5.04--6.97% across the six reported metrics; on Youshu, HED-64 improves by 1.87--4.56%. Ablation results support the contributions of both the user--bundle branch and intra-type relations, and sensitivity analyses identify stable operating ranges for the main hyperparameters. We further quantify the computational trade-off of the complete hypergraph, including its memory cost. The evidence supports HED on the two evaluated bundle-recommendation datasets while making its resource limitations explicit. Code and datasets will be made available upon publication.